Simulating a continous distribution

[MechatronO]

Say we want a set of random values that are distributed according to some distribution function f(x).

A common way to accomplish that is to find the cumulative distribution function F(x) for the distribution and then solve for x according to

F(x) = Y

x = F'(Y)

Then x will be distributed with the original distribution function, if F'(Y) is fed with random values Y ranging from 0-1.

I'm currently trying to do that with a weibull distribution

f(x) = a*b*x^b-1*e^{-a*b*x^b}

where F(x) should be

F(x) = e^-a - e^{-a*x^b}

when solving for x in F(x) I however get

x = ( - ln(e^-a - Y)/a)^1/b

When Y> e^-a there are no real solutions. Is there a way to get around this? Have I done something wrong?

 

[mathman]

Your F(x) can't be right. F(∞) should be 1.